#### DMCA

## Computational Methods for Global Illumination and Visualisation of Complex 3D Environments

### BibTeX

@MISC{n.n._computationalmethods,

author = {n.n.},

title = {Computational Methods for Global Illumination and Visualisation of Complex 3D Environments},

year = {}

}

### OpenURL

### Abstract

Complex three dimensional environments are visualised by rendering images of these environments as seen from different view points. Over the last three decades rendering techniques have been continuously evolving to greater levels of sophistication in terms of the complexity of environments and the realism with which the images are produced. In all image synthesis techniques the fundamental step is computation of the amount and nature of the light from the three dimensional environment reaching the eye in any given direction. Computer graphics rendering techniques carry out this computation by simulating the behaviour of light in the environment. Greater degrees of realism would mean higher correlation between the simulation and the physical world. In the physical world, lighting, reflection and scattering effects are very complicated and subtle. Every object receives light directly from light sources, or indirectly from reflection or scatter by other neighbouring objects. For realistic image synthesis these intra-environmental effects must be modelled in great detail. This thesis presents the results of a detailed investigation of illumination computation and rendering techniques. The four major contributions of this thesis are: A taxonomy of illumination computation methods. Particle tracing techniques for global illumination computation. The potential equation for illumination computation and the mathematical framework of adjoint equations. Demonstration of the practicality of this new class of global illumination computation algorithms. From a theoretical point of view the primary contribution is the development ofa mathematical framework of adjoint equations which provides the basis for all known illumination computation techniques. This mathematical framework consists of two integral equations- the radiance and the potential equation, which are duals of each other. While the radiance equation has been known in one form or the other to the computer graphics community, the potential equation for illumination has been introduced for the first time in this thesis. The signi cance and importance of this new mathematical framework stems from the fact that it not only enables us to review and analyse existing methods but also provides the necessary handles for deriving new and

### Keyphrases

mathematical framework computational method potential equation global illumination physical world adjoint equation illumination computation dimensional environment intra-environmental effect great detail new class global illumination computation algorithm object receives detailed investigation signi cance computer graphic community different view point theoretical point illumination computation method realistic image synthesis necessary handle major contribution computer graphic primary contribution image synthesis scattering effect greater degree fundamental step radiance equation integral equation illumination computation technique global illumination computation first time new mathematical framework light source neighbouring object